Yes you add your Dexterity modifier to AC, except in the case of wearing or using a particular sort of armor option that imposes a Dex Cap.
Yes, mage armor cast as a 1st level spell provides +1 to AC. With it having that AC bonus, a Dex Cap of +5, no check penalty, and allowing use of your unarmored defense proficiency instead of light armor or something it is better protection than leather armor - and once you can cast it as a higher level spell, the benefits are even greater.
Don't forget that the equipment and ability score portions of AC end up being the smaller portions in this edition because of adding your level (plus 2 or more) for proficiency.
